Rapidly tunable, narrow-band infrared filter arrays

ABSTRACT

Tunable filters can use Fano metasurface designs having extremely narrow transmission bands. The Fano metasurface can comprise dielectric or semiconductor materials and can produce transmission bands with quality factors well in excess of 1000—at least a factor of 50 greater than typical metamaterial-based infrared resonances. Numerical simulations of these metasurfaces show that the spectral position of the passband can be changed by slightly changing the position of a small dielectric perturbation block placed within the near-field of the resonator by using simple electromechanical actuation architectures that allow for such motion. An array of independently tunable narrowband infrared filters can thereby be fabricated that only requires deep-subwavelength motions of perturbing objects in the resonator&#39;s near-field.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of U.S. application Ser. No. 15/227,440, filed Aug. 3, 2016, which claims the benefit of U.S. Provisional Application No. 62/212,258, filed Aug. 31, 2015, both of which are incorporated herein by reference.

STATEMENT OF GOVERNMENT INTEREST

This invention was made with Government support under Contract No. DE-NA0003525 awarded by the United States Department of Energy/National Nuclear Security Administration. The Government has certain rights in the invention.

FIELD OF THE INVENTION

The present invention relates to infrared filter arrays and, in particular, to a rapidly tunable, narrow-band infrared filter array based on a Fano metasurface.

BACKGROUND OF THE INVENTION

Metasurfaces are the two-dimensional surface counterparts of the fully three-dimensional bulk metamaterials. Metasurfaces are currently the subject of intensive research worldwide since they can be tailored to produce a wide range of optical behaviors. However, metasurfaces generally exhibit broad spectral resonances, and it is difficult to obtain narrow (i.e. high quality-factor, Q) spectral features. Attaining such high-Q features from metasurfaces would greatly expand their application space, particularly in the areas of sensing, spectral filtering, and optical modulation. Early metasurfaces were fabricated from metals and exhibited particularly broad resonances at infrared and optical frequencies as a result of Ohmic losses. Dielectric resonator-based metasurfaces were introduced to overcome these losses and have enabled, among others, wave-front manipulation and cloaking devices, perfect reflectors, and ultrathin lenses but, although absorptive losses were reduced, the metasurface resonances remained broad due to strong coupling with the external field (i.e. large radiation losses). See J. C. Ginn et al., Phys. Rev. Lett. 108 (9), 097402 (2012); I. Staude et al., ACS Nano 7 (9), 7824 (2013); A. Arbabi et al., Nat. Nano 10 (11), 937 (2015); S. Jahani and Z. Jacob, Nat. Nano 11 (1), 23 (2016); M. I. Shalaev et al., Nano Lett. 15 (9), 6261 (2015); K. E. Chong et al., Nano Lett. 15 (8), 5369 (2015); D. Lin et al., Science 345 (6194), 298 (2014); L. Y. Hsu et al., Prog. Electromagn. Res. 152, 33 (2015); P. R. West et al., Opt. Express 22 (21), 26212 (2014); and P. Moitra et al., ACS Photonics 2 (6), 692 (2015).

Recently, new strategies based on “electromagnetically induced transparency” or “Fano resonances” have been developed that show great promise for achieving high-Q resonances. See C. Wu et al., Nat. Mater. 11 (1), 69 (2012); R. Singh et al., Appl. Phys. Lett. 105 (17), 171101 (2014); C. Wu et al., Nat. Commun. 5, (2014); Y. Yang et al., Nat. Commun. 5, (2014); and W. Zhao et al., Opt. Express 23 (5), 6858 (2015). In this approach, the resonator system is designed to support both “bright” and “dark” resonances. The incident optical field readily couples to the bright resonance, but cannot couple directly to the dark resonance. Through proper design, a weak coupling between the two resonances can be introduced, allowing energy from the incident wave to be indirectly coupled to the dark resonance. The metasurface transmission and reflection spectra resulting from such an approach feature Fano resonances that can be much narrower than the traditional metasurface resonances. This approach has been demonstrated for metal-based metasurfaces at THz frequencies where Q-factors approaching 100 have been observed. See C. Wu et al., Nat. Mater. 11 (1), 69 (2012); and R. Singh et al., Appl. Phys. Lett. 105 (17), 171101 (2014).

Even more dramatic results have been achieved by applying this strategy to dielectric resonator-based metasurfaces and Q-factors approaching 500 have been demonstrated. See Y. Yang et al., Nat. Commun. 5, (2014). A common feature of the dielectric resonator-based Fano designs demonstrated thus far is the reliance on multiple, distinct, near-field coupled dielectric structures within the unit cell. See Y. Yang et al., Nat. Commun. 5, (2014); W. Zhao et al., Opt. Express 23 (5), 6858 (2015); and F. Wang et al., Opt. Mater. Express 5 (3), 668 (2015). However, reliable and repeatable control of near-field coupling requires exacting fabrication tolerances.

Further, a need remains for a rapidly tunable, narrowband filter array that can be integrated with infrared (IR) focal plane arrays for a wide range of imaging and sensing applications. Current state-of-the-art for tunable focal plane filter arrays relies on microelectromechanical systems (MEMS)-based Fabry-Perot filters which produce spectrally broad transmission pass bands. See W. J. Gunning et al., Proc. SPIE 5783, 366 (2005). Furthermore, the tunable Fabry-Perot infrared filter array requires MEMS-based motion over large distances (of order the wavelength) to tune the spectral passband. Other approaches include liquid crystal devices, which are slow, lossy, and don't achieve narrow passbands; phase change materials such as VO₂, which are not continuously tunable and do not produce desirable passband spectral profiles; and metasurface arrays fabricated on stretchable membranes, which rely on the impractical tuning mechanism of stretching. See H. Zhang et al., Appl. Opt. 53, 5632 (2014); H. Kocer et al., Appl. Phys. Lett. 106, 161104 (2015), and I. M. Pryce et al., Nano Lett.10, 4222 (2010).

SUMMARY OF THE INVENTION

The present invention is directed to a rapidly tunable, narrow-band filter array that can be integrated with IR focal plane arrays. The tunable filter is based on a new, monolithic all-dielectric resonator metasurface that yields high quality-factor Fano resonances. The invention utilizes perturbations of high-symmetry resonator structures to induce couplings between the otherwise orthogonal resonator modes. In particular, the perturbations couple “bright” dipole modes to “dark” dipole modes whose emission is suppressed by local field effects. Numerical simulations of these Fano metasurfaces show that the spectral position of the passband can be changed by slightly changing the position of a small dielectric perturbation, such as a block, placed within the near-field of the resonator. Therefore, these metasurfaces can be made with spectral tunability by using simple electromechanical actuation architectures that allow for such motion. In particular, deep-subwavelength motions of dielectric blocks in the resonator's near-field can provide an array of independently tunable narrowband infrared filters. This device is superior to the Fabry-Perot approach because it requires significantly less MEMS-based motion and can achieve significantly narrower transmission linewidths. For example, simulations of a Fano metasurface-based tunable filter array operating in the thermal infrared (8-12 μm) show that Fano resonance can shift by many multiples of its linewidth. These infrared filter arrays can be coupled with infrared focal plane arrays to enable a wide range of infrared imaging and sensing capabilities.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description will refer to the following drawings, wherein like elements are referred to by like numbers.

FIGS. 1A and 1 b are schematic illustrations depicting the operating principles of the Fano metasurfaces. FIG. 1A shows that the electric field of the incident radiation excites only the p_(x) electric dipole mode of the cube resonators (dark arrows). The decay of the electric dipole mode is governed by both radiative (r) and non-radiative (nr) processes. FIG. 1B shows how symmetry breaking can be used to allow coupling of the p_(x) dipole to the longitudinal m_(z) magnetic dipole (dark loops) which only decays due to non-radiative losses (neglecting the small coupling to radiating moments). A similar process (not shown) involving the bright in-plane magnetic dipole (m_(y)) and dark longitudinal electric dipole (p_(z)) leads to a second Fano resonance at higher energy.

FIG. 2 is a perspective view schematic illustration of the unit cell of a germanium Fano metasurface design. The period of the metasurface is 4.2 μm.

FIG. 3 is the reflectivity spectrum of the array in FIG. 2 obtained using full-wave simulations. The inset on the left shows an expanded view of the resonance at ˜10.8 μm. The Q-factor for this resonance is ˜1300. The inset on the right shows a vector plot of the electric field in the x-y resonator mid-plane featuring a circulating pattern.

FIG. 4 is a graph of the power radiated by the four dominant multipoles of the Fano resonators when excited in the array (no substrate). At the resonant frequency the x-directed electric dipole is largely extinguished and the z-directed magnetic dipole dominates.

FIG. 5 is a graph of the absolute magnitude of the magnetic field enhancement for the centermost resonator as a function of array size. The enhancement rises sharply with array size for the smaller arrays, and is beginning to saturate at the largest (9×9) array. The overall size of the array required to achieve a robust Fano resonance is quite small.

FIG. 6 is a perspective view schematic illustration of an exemplary silicon-on-insulator resonator array Fano metasurface. The period of the metasurface is 550 nm.

FIG. 7 is the experimentally measured reflectivity spectrum of the Si resonator array shown in the inset. The Q-factor for the resonance at 998.8 nm is ˜350.

FIG. 8 is a perspective view schematic illustration of an exemplary GaAs-based Fano metasurface.

FIG. 9 is a graph of the measured reflectivity spectrum from three GaAs-based Fano metasurfaces with slightly different in-plane scalings (s) of a nominal 270×270×300 nm³ design. The array corresponding to the largest scaling factor exhibits a resonance with a FWHM of 1.6 nm, corresponding to a Q-factor of approximately 600. The inset shows an SEM of several of the resonators in the s=0.95 array.

FIG. 10A is a schematic illustration of normal tuning of a Fano metasurface-based tunable filter array. The Fano transmission resonance shifts as the perturbing block moves in a direction normal to the resonator face. FIG. 10B is a schematic illustration of lateral tuning. Moving the perturbing block laterally from a high symmetry position causes the Fano transmission resonance to appear. The spectral position of the resonance depends on the magnitude of the lateral shift.

FIGS. 11A and 11B are schematic Illustrations of MEMS-like actuation for vertical tuning the Fano resonances of an array. FIG. 11A shows the perturbing blocks in a near-field position. FIG. 11B shows vertical tuning by collectively moving all the perturbing blocks downward from the cubic resonators.

FIGS. 12A and 12B are schematic Illustrations of MEMS-like actuation for lateral tuning the Fano resonances of an array. FIG. 12A shows the perturbing blocks in a near-field position. FIG. 12B shows lateral tuning by collectively moving all the perturbing blocks laterally with respect to the cubic resonators.

FIGS. 13A and 13B are schematic illustrations of a vertically tuned Fano metasurface. FIG. 13A shows the perturbing block initially in the near field of the dielectric resonator. FIG. 13B shows the perturbing block in a position that destroys the asymmetry of the resonator, and hence the Fano resonance.

DETAILED DESCRIPTION OF THE INVENTION

Dielectric resonators are generally fabricated from high permittivity materials, such as Te, Ge, GaAs, Si, or PbTe, so that the dimensions of the resonator are smaller than the free-space wavelength at the resonator's resonant frequencies (as used herein, “dielectric” can include both insulating and semiconducting materials). Dielectric resonators are generally fabricated using symmetric geometries such as cubes or spheres. However, a symmetric geometry is not required provided the resonator supports an in-plane dipole mode (electric or magnetic) that can couple to incoming and outgoing plane waves. The resonant modes of symmetric resonators are orthogonal and do not couple to each other. However, certain classes of perturbations to the resonator geometry can induce coupling between the otherwise orthogonal modes. For example, one of a cubic resonator's side walls can be tilted (either in-plane or out-of-plane), or a notch can be cut near one edge of the resonator. Other geometric perturbations are possible. In addition, the perturbation can utilize other dielectric materials that are distinct from the material from which the resonator is fabricated. For example, the “notch” cut from the edge of the resonator can be filled with a different material with a larger or smaller permittivity than that of the dielectric resonator structure. The perturbation can also comprise an anisotropic material coupling to the out-of-plane moments. When perturbed in this manner, the in-plane and out-of-plane modes largely retain their character (i.e. the z-directed magnetic dipole of the symmetric resonator still has the character of a z-directed magnetic dipole in the perturbed resonator).

Dielectric resonator metasurfaces are two-dimensional, periodic arrays of dielectric resonators. The metasurfaces are non-diffractive when the period of the array is smaller than the free-space wavelength. In this case the arrays can be optically characterized by their transmission and reflection spectra. For symmetric resonators, the metasurfaces will exhibit broad spectral regions of high reflectivity at the electric and magnetic dipole resonances. However, metasurfaces of properly perturbed resonators will feature extremely sharp spectral transmission resonances in addition to the broad reflection peaks.

This new metasurface design relies on a single resonator per unit cell and produces robust, high quality-factor Fano resonances. The metasurface utilizes symmetry breaking of highly symmetric resonator geometries, such as a cube, sphere, prism, pyramid, or cylinder, to induce couplings between the otherwise orthogonal resonator modes. In particular, the perturbations couple “bright” dipole modes to “dark” dipole modes whose radiative decay is suppressed by local field effects in the array. The design is widely scalable from the near-infrared to radio frequencies (e.g., 0.75 μm to 1 m wavelength). The resonator can comprise a high permittivity or high refractive index material (the permittivity, ε, and refractive index, n, are related by ε=n² in non-magnetic materials), such as Te, Ge, Si, or a IV-VI compound comprising lead, such as PbTe. Alternatively, the resonator can comprise a III-V compound having a high refractive index, such as GaAs, GaN, or other III-V alloys. An array of such resonators can be fabricated on a low-loss substrate having a lower refractive index than the resonator material. For example, both silicon dioxide and barium fluoride have a refractive index of about 1.45 in the near-infrared. When these materials are used as a substrate, the refractive index of the resonator should be greater than about 2.5. For example, the resonator can comprise Si or GaAs which have refractive indices of about 3.5 in the near-infrared. If a high index substrate is used, the substrate can further comprise an intermediate layer having a low refractive index that can be used to separate the high index dielectric resonator from the high index substrate so that the mode is still confined within the resonator.

As described below, Fano resonance behavior is demonstrated through numerical simulations of a germanium resonator-based metasurface that achieves a quality-factor of ˜1300 at ˜10.8 μm. As examples, two metasurfaces were fabricated that operate in the near-infrared (˜1 μm): a silicon-based metasurface that achieves a quality-factor of ˜350; and a gallium arsenide-based metasurface that achieves a quality-factor of ˜600. In both examples, large electromagnetic field enhancements appear within the resonators at the Fano resonant frequencies. Combining high quality-factor, high field enhancement resonances with nonlinear and active/gain materials, such as gallium arsenide, can provide new classes of active optical devices.

The principles underlying the high-Q Fano metasurface are shown schematically in FIGS. 1A and 1B. An exemplary resonator design starts with a simple cubic resonator similar to the dielectric resonators demonstrated in J. C. Ginn et al. See J. C. Ginn et al., Phys. Rev. Lett. 108 (9), 097402 (2012). For an isolated resonator, such a high-symmetry geometry leads to orthogonal, but degenerate, sets of electric and magnetic dipole modes oriented along the x-, y- and z-directions (along with other higher order multipoles). When arranged in an array with subwavelength periodicity, only the transverse (i.e. in-plane) dipole modes can couple to a normally incident electromagnetic wave, as shown in FIG. 1A, and this results in the usual (broad) electric and magnetic transmission/reflection resonances. See J. C. Ginn et al., Phys. Rev. Lett. 108 (9), 097402 (2012), which is incorporated herein by reference. However, it is possible to “perturb” the geometry to change the spectral positions of the modes, or even to induce mode mixing between the transverse and longitudinal dipole modes. See L. K. Warne et al., Prog. Electromagn. Res. B 44, 1 (2012); L. K. Warne et al., IEEE Trans. Antennas Propagat. 61 (4), 2130 (2013); S. Campione et al., Opt. Express 23 (3), 2293 (2015); and U.S. Pat. No. 9,374,887, each of which is incorporated herein by reference. FIG. 1B shows a symmetry breaking induced coupling between the p_(x) electric dipole mode and the longitudinal m_(z) magnetic dipole mode. While the p_(x) dipole is subject to both radiative and non-radiative decay processes, the m_(z) mode is subject to only non-radiative decay and high Q-values can be achieved using low-loss dielectric materials. The interference between these two modes leads to the observed high-Q Fano resonances. A similar process (not shown) involving the bright in-plane magnetic dipole (m_(y)) and dark longitudinal electric dipole (p_(z)) leads to a second Fano resonance at higher energy.

FIG. 2 is a schematic illustration of such a broken symmetry resonator design that utilizes germanium as the resonator material. Starting with a cubic geometry of nominal side length 2.53 μm, a small notch is cut from one corner of the cube and the adjacent corner has been slightly extended. The resonators are arrayed on a barium fluoride (BaF₂) substrate with an array period of 4.2 μm. Such a low index substrate is necessary to retain the original Mie modes of the dielectric resonators. See J. C. Ginn et al., Phys. Rev. Lett. 108 (9), 097402 (2012).

FIG. 3 shows the reflectivity spectrum of the germanium resonator array under x-polarized incidence obtained from a Finite Difference Time Domain (FDTD) simulation. Several extremely narrow Fano resonances are observed—the transmission spectrum (not shown) exhibits complementary (pass-band) transmission resonances. Note that the Ge properties used in the simulations included the appropriate material absorptive loss values. The quality-factor of the Fano reflection resonance (as defined by λ₀/Δλ where λ₀ is the resonant frequency and Δλ, is the full width at half minimum (FWHM) of the resonance) at ˜10.8 μm exceeds 1300. Furthermore, at the Fano resonant frequency, the electric and magnetic fields within the resonator are enhanced by several orders of magnitude relative to the incident field (not shown here).

The inset of FIG. 3 shows a vector plot of the electric field in the x-y plane located half way through the resonator and calculated at the Fano resonance at 10.8 μm. The circulating electric field seen in the inset is reminiscent of a magnetic dipole field pattern; however, rather than the usual in-plane magnetic dipole, the orientation of the resonant dipole is out of the plane of the array (i.e. a z-directed magnetic dipole). To further confirm this assignment, the following “numerical experiment” was performed. First, the on-resonance response of the array was simulated (without a substrate for simplicity), placing a fictitious box around the center resonator of the array. Using Love's Equivalence Principle, the sources within the box (i.e. the central resonator) were replaced with equivalent electric and magnetic surface currents derived from the total tangential fields on the box. All the other resonators in the array were removed and the fields radiated by the surface currents on the box were calculated. The radiated far-fields were then decomposed into their multipole components including all the quadrupole contributions. See S. Campione et al., Opt. Express 23 (3), 2293 (2015). FIG. 4 shows the power radiated by the dominant four multipoles (the powers of the multipole components not shown in the figure are several orders of magnitude smaller than the dominant multipoles). Above and below the resonant frequency of ˜27.8 THz (˜10.8 μm), the x-directed electric dipole (p_(x)) dominates, as expected. However, in the vicinity of the Fano resonance the strength of p_(x) decreases dramatically. Simultaneously, the strength of the z-directed magnetic dipole (m_(z)) increases remarkably and dominates all other multipoles by nearly two orders of magnitude. This excitation occurs indirectly, through coupling to the x-directed electric dipole. This confirms the earlier assignment of the resonant mode as m_(z). Note also that at the resonant frequency the y-directed electric dipole (p_(y)) and the z-x magnetic quadrupole (M_(zx)) are also excited. However, the fields radiated by p_(y) and M_(zx) largely cancel each other in the forward and backward directions, which, in combination with the dramatic decrease of p_(x), explains the high transmission and low reflection observed at the Fano resonance. The lack of perfect cancellation between p_(y) and M_(zx) results in a small depolarization of the transmitted wave. The reflection spectrum shown in FIG. 3 exhibits an additional Fano resonance at shorter wavelengths. A similar analysis shows that the origin of the higher energy Fano resonance appearing at ˜9.7 μm in this figure is analogous to the mechanism described above. However, in this case the bright mode is an in-plane magnetic dipole (m_(y)) and the dark mode is a longitudinal electric dipole (p_(z)).

The excitation of the m_(z) multipole likely arises due to the different widths (in the x-direction) of the two parts of the resonator. Considering each part of the resonator as a separate polarizable dielectric region, it can be seen that such an approximate spatial decomposition indicates the two separated electric dipoles will exhibit slightly different dipole strengths. Upon excitation with an x-polarized wave, the asymmetry of the two dipoles will lead to a z-directed magnetic field in the vicinity of the center of the resonator which can couple to and excite the m_(z) dipole. Such an excitation mechanism is unavailable for the symmetric full cube resonator.

The large Q-factors of the Fano resonances arise due to the small radiative and non-radiative decay rates of the z-directed magnetic dipole in the array. For an isolated resonator, the z-directed dipole is free to radiate and is also subject to non-radiative decay processes arising from material absorption. This results in broad resonance linewidths for the isolated resonator. In contrast, when placed in the two-dimensional array, the resonator's normal radiative decay is compensated by driving terms arising from the local field at the position of the resonator, leaving only the (small) non-radiative processes. See S. Tretyakov, Analytical Modeling in Applied Electromagnetics, London, UK: Artech House (2003); and J. E. Sipe and J. V. Kranendonk, Phys. Rev. A 9 (5), 1806 (1974). Thus, the overall Q-factor of the resonators, and hence the Q-factor of the Fano resonance, becomes large. To demonstrate the importance of array effects in establishing the Fano resonance, the response of finite sized arrays (no substrate for simplicity) of varying sizes was simulated. For the isolated resonator, no Fano resonance is observed and the electric field vector plots are reminiscent of a p_(x) excitation. For the other simulations, the frequency of the Fano resonance shifts slightly as the array size increases. The 3×3 array shows a very weak Fano resonance, and the on-resonance electric field vector plots are complicated but begin to show field circulation within each resonator. The 5×5 array exhibits a clear Fano resonance, and the vector field plots for the interior resonators clearly show the electric field circulation associated with the m_(z) dipole. Interestingly, the innermost resonator of the array shows the largest field enhancement, while the resonators at the edge of the array (which experience a drastically different local field and can radiate substantially more) show smaller field enhancements and less well defined modes. Proceeding to the 7×7 and 9×9 arrays, the number of interior resonators experiencing large field enhancements increases with array size, and once again the outermost resonators show weaker excitations. The absolute magnitude of the field enhancement for the centermost resonator rises sharply with array size for the smaller arrays, and is beginning to saturate at the largest (9×9) array, as shown in FIG. 5. Thus, the overall size of the array required to achieve a robust Fano resonance is quite small.

As an example of the invention, a silicon-based Fano metasurface operating near 1 μm wavelength was designed and fabricated, as shown in FIG. 6. The resonators were fabricated using silicon-on-insulator wafers with a 250 nm thick silicon layer. The nominal side length of the resonators was 280 nm and the array spacing was 550 nm. The arrays were fabricated using e-beam lithography and reactive ion etching. Reflectivity spectra were measured using a custom built near-infrared polarizing microscope coupled to a high-resolution spectrometer equipped with a CCD array detector. The inset of FIG. 7 shows a scanning electron micrograph (SEM) of several of the resonators in the array, along with the experimentally measured reflectivity spectrum. The measured spectrum shown in FIG. 7 is very similar to the simulated spectrum (not shown), although an overall wavelength shift is observed. This shift is attributed to slight dimensional differences between the designed and fabricated arrays. The measured quality-factor of the resonance at 998.8 nm is about 350. There is also a slight difference between the simulated and measured spectra in the shape of the shorter wavelength Fano resonance that is likely due to a small inaccuracy in the SOI buried oxide thickness used in the simulations. The buried oxide forms a low finesse etalon that interferes with the Fano behavior and modulates the overall shape of the resonance.

For another example of the broken symmetry Fano approach, a GaAs-based Fano metasurface was fabricated by adapting a processing scheme originally developed for surface emitting semiconductor lasers. See K. D. Choquette et al., IEEE J. Sel. Topics Quantum Electron. 3 (3), 916 (1997); and K. D. Choquette et al., IEEE Photon. Technol. Lett. 7 (11), 1237 (1995). In contrast to indirect bandgap Si used in the experimental demonstration described above, GaAs features a direct bandgap so that residual absorptive losses should be smaller in the near-infrared spectral range and larger Q-values might be possible. The resonator arrays were fabricated using epitaxially-grown GaAs layers and employ a novel means of isolating the resonators from the native GaAs substrate on which they were grown with a resonator-shaped AlGaO intermediate layer (alternatively, a continuous AlGaO intermediate layer could be used). Three GaAs Fano resonators with the same array pitch of 470 nm and height of 300 nm but different in-plane unit cell dimensional scaling factors of s=0.89, 0.92, and 0.95. FIG. 8 shows a schematic of the unit cell with a scaling factor of 1 that comprises a cuboid with nominal side length of 270 nm and a smaller cuboid notch with side dimensions of x=70 nm and y=190 nm cutting through the resonator.

FIG. 9 shows the experimental reflectivity spectrum for three GaAs Fano metasurfaces with slightly different in-plane dimensional scaling factors, s, of a nominal 270×270×300 nm³ (s=1.0) design. As expected, the Fano resonances shift to longer wavelength as the scaling factor increases. Notably, the FWHM of the Fano resonance is 1.6 nm for the metasurface corresponding to the largest scaling factor. This corresponds to a Q-factor of ˜600. Low temperature reflectivity measurements (not shown here) showed a shifting of the spectral location of the Fano resonance, but did not reveal any further narrowing of the resonance. The achievement of such high-Q resonances along with their large field enhancements in GaAs is particularly exciting since it opens up new avenues for device designs that exploit the active and nonlinear properties of GaAs.

Tunable, Narrowband Filter Array

Tunable filters can use the Fano metasurface designs having extremely narrow transmission bands. As described above, the Fano metasurface can comprise dielectric or semiconductor materials, such as Si, GaAs, and Ge, and can produce transmission bands with quality factors well in excess of 1000—at least a factor of 50 greater than typical metamaterial-based IR resonances. Numerical simulations of these metasurfaces show that the spectral position of the passband can be changed by slightly changing the position of a small dielectric perturbation block placed within the near-field of the resonator. These metasurfaces can provide spectral tunability by using simple electromechanical actuation architectures that allow for such motion. Thereby, an array of independently tunable narrowband infrared filters can be fabricated that only requires deep-subwavelength motions of perturbing objects in the resonator's near-field.

The narrowband tunable filter arrays of the present invention are based upon the Fano metasurfaces described above. In these metasurfaces, a symmetry breaking perturbation of the resonator structure introduces a weak coupling between an incident wave and an extremely high Q-factor magnetic dipole mode. This mode is completely uncoupled from external radiation in the unperturbed symmetric resonator. The weak coupling results in the appearance of sharp Fano resonances in the transmission and reflection spectra of metasurface arrays. For example, consider the Fano resonator design based upon germanium shown in FIG. 2. The simulated transmission spectrum of the metasurface array, shown in FIG. 3, exhibits extremely narrow transmission resonances in the thermal IR (and complementary reflection notches) with Q-factors in excess of 1000. The magnitude and width of the passband can be adjusted by changing the strength of the symmetry breaking. The inset of FIG. 3 shows the electric field pattern at the mid-plane of the resonator exhibits a circulating behavior that is characteristic of a z-directed magnetic dipole. This Fano metasurface design is scalable from near-IR to microwave wavelengths and can be implemented using other high permittivity materials. As described above, exemplary Fano metasurfaces based on Si resonators and GaAs resonators have been fabricated that operate in the near-IR.

The resonator shown in FIG. 2 uses a cut corner as the source of the symmetry breaking. However, symmetry breaking can also be introduced by perturbing objects that don't physically touch the resonator, but rather are placed in the resonator's near-field (e.g., hundreds of nanometers). FIGS. 10A and 10B show the results of full-wave electromagnetic simulations of a symmetric resonator that has a small “perturbing block” located in a symmetry breaking position in the near-field. As with the monolithic resonator of FIG. 2, a sharp Fano resonance appears in the transmission spectrum. Increasing the gap between the perturbing block and the cube causes a continuous shifting of the

Fano resonance (termed “normal tuning”). In the example shown in FIG. 10A, a small 300 nm movement of the block normal to the resonator causes the Fano resonance to shift by many multiples of its linewidth from the zero gap position. A second example of on/off resonance tuning is shown in FIG. 10B. In this case, the perturbing block is first placed in a high symmetry position along the centerline of the resonator. In this example, no Fano resonance is observed (“centered” curve) when the block is in the centerline position. Moving the perturbing block laterally, to a lower symmetry position, results in the appearance of the Fano transmission resonance (“offset” curve). The spectral location of the Fano resonance will also tune as the lateral displacement is varied (termed “lateral tuning”). Numerical simulations have also shown that tuning can be achieved through vertical motion of the perturbing block (vertical tuning). These examples show that the required symmetry breaking can be achieved in a variety of ways, including combinations of normal, vertical, and lateral tuning. In principle, the resonator can be any symmetric structure, such as a cube, sphere, a prism, a pyramid, or a cylinder, and the perturbation can be any movable object, such as a straight, tilted, or stepped dielectric block, metallic decoration, liquid droplet, etc. Preferably, the design provides large tuning of the transmission band, while still maintaining small overall displacements of the perturbing block.

A MEMS-like electrostatic actuator can be used to achieve the desired motion of the perturbing block. FIGS. 11A and 11B show schematic illustrations of an exemplary device for achieving vertical motion of the perturbing block. FIG. 11A shows a tunable array 10 in which the perturbing blocks are in unactuated positions relative to the cubic dielectric resonators. Each block 12 is in the near-field on an adjacent dielectric resonator 11. FIG. 11B shows an array 10′ in which the perturbing blocks 12 are in actuated positions relative to the cubic resonators 11. Each block 12 has been moved normally and vertically with respect to the adjacent dielectric resonator 11 by a cantilever-type actuator arm 13, which will result in a shift in the Fano resonance. The actuator arm 13 can be driven, for example, by an electrostatic actuator.

FIGS. 12A and 12B show schematic illustrations of an exemplary device for achieving lateral motion of the perturbing block. FIG. 12A shows a tunable array 20 in which the perturbing blocks 22 are in a symmetric, unactuated positions relative to the cubic dielectric resonators 21. Each block 22 is in the near-field of an adjacent dielectric resonator 21. FIG. 11B shows an array 20′ in which lateral tuning is achieved by collectively moving all the perturbing blocks 22 laterally with respect to the cubic dielectric resonators 21 with an actuator arm 23. The actuator arm 23 can be driven, for example, with a comb-drive actuator.

FIGS. 13A and 13B show side-view schematic illustrations of two resonators of an exemplary tunable array that can be fabricated using surface and bulk silicon micromachining. In order to avoid issues with stiction, the perturbing block 32 moves out of the near field of the dielectric resonator 31 when actuated, rather than moving into the near field and risking contact. To fabricate the array 30, alternating ground/supply polysilicon traces 34, 35 can be deposited on a silicon nitride-coated silicon wafer 37. The silicon nitride 36 serves as an intermediate and routing layer to affect electrostatic tuning. A polysilicon stub 38 contacts to the supply traces 35, upon which the polysilicon resonator 31 can be built up. A perturbing polysilicon block 32 can be formed in the same layer as the polysilicon resonators 31, but positioned over the ground trace 34 without a stub connection. After backfill with sacrificial oxide, thin, conductive polysilicon tethers 33 can be deposited, each forming a flexible cantilever arm that also electrically connects a neighboring resonator with the perturbing block 32. After patterning the tethers, the sacrificial oxide can be removed with hydrofluoric acid. An actuator can be provided to move the block relative to the resonator (or vice versa). For example, the actuator can conveniently be a simple electrostatic actuator (as shown), although other types of micro actuators (e.g., comb drive, magnetic, thermal, piezoelectric, shape memory, or pneumatic actuator) can also be used. As shown in FIG. 12A, the perturbing block 32 is initially in the near field of the adjacent resonator 31. By applying a voltage between the routing layer traces 35 at the periphery of the array, an electrostatic potential can be formed between the perturbing block 32 and the ground trace 34, causing the block 32 to deflect downward, as shown in FIG. 12B, destroying the asymmetry of the resonator, and hence the Fano resonance. Note that the block 32 need not actually contact the ground trace 34.

The present invention has been described as a rapidly tunable, narrow-band infrared filter array. It will be understood that the above description is merely illustrative of the applications of the principles of the present invention, the scope of which is to be determined by the claims viewed in light of the specification. Other variants and modifications of the invention will be apparent to those of skill in the art. 

We claim:
 1. A tunable filter array, comprising: a Fano metasurface, comprising: a periodic two-dimensional array of dielectric resonators on a dielectric substrate, and a perturbing object within the near field of each dielectric resonator, wherein each dielectric resonator has an electric or magnetic dipole moment in the plane of the dielectric substrate that couples to normally incident light and wherein the perturbing object induces coupling of at least one out-of-plane electric or magnetic dipole moment in the near-field to the in-plane electric or magnetic dipole moment, whereby the out-of-plane electric or magnetic dipole moment provides a narrow spectral resonance within a broad spectral resonance provided by the in-plane electric or magnetic dipole moment; and an actuator for moving each perturbing object relative to each dielectric resonator, whereby the narrow spectral resonance can be tuned by moving the perturbing objects relative to the dielectric resonators.
 2. The tunable filter array of claim 1, wherein the dielectric resonators comprise germanium, tellurium, silicon, or a IV-VI compound comprising lead.
 3. The tunable filter array of claim 1, wherein the dielectric resonators comprise a III-IV compound.
 4. The tunable filter array of claim 3, wherein the III-V compound comprises gallium arsenide or gallium nitride.
 5. The tunable filter array of claim 1, wherein the dielectric substrate comprises a material having a lower permittivity than the permittivity of the dielectric resonators.
 6. The tunable filter array of claim 5, wherein the dielectric resonators comprise Ge and dielectric substrate comprises BaF_(2.)
 7. The tunable filter array of claim 1, wherein the dielectric substrate further comprises an intermediate layer having a lower permittivity than the permittivity of the dielectric resonator.
 8. The tunable filter array of claim 7, wherein the dielectric resonators comprise silicon and the intermediate layer comprises silicon nitride.
 9. The tunable filter array of claim 7, wherein the dielectric resonators comprise GaAs and the intermediate layer comprises AlGaO.
 10. The tunable filter array of claim 1, wherein the incident light has a wavelength between 0.75 μm and 1 m.
 11. The tunable filter array of claim 10, wherein the incident light has a wavelength between 8 μm and 12 μm.
 12. The tunable filter array of claim 11, wherein the tunability of the narrow spectral resonance is up to 1 μm.
 13. The tunable filter array of claim 1, wherein the narrow spectral resonance has a Q-factor of greater than
 100. 14. The tunable filter array of claim 1, wherein the dielectric resonators comprise a cube.
 15. The tunable filter array of claim 1, wherein the dielectric resonators comprise a sphere, a prism, a pyramid, or a cylinder.
 16. The tunable filter array of claim 1, wherein the perturbing object comprises a block.
 17. The tunable filter array of claim 16, wherein each block is moved normally with respect to each dielectric resonator.
 18. The tunable filter array of claim 16, wherein each block is moved laterally with respect to each dielectric resonator.
 19. The tunable filter array of claim 16, wherein each block is moved vertically with respect to each dielectric resonator.
 20. The tunable filter array of claim 1, wherein the size of each dielectric resonator is subwavelength to the incident light.
 21. The tunable filter array of claim 1, wherein the size of the periodic two-dimensional array is greater than a 5×5 array. 